Switchable achromatic compound retarder

ABSTRACT

This invention provides achromatic liquid crystal compound retarders, achromatic polarization switches, and achromatic shutters using the liquid crystal compound retarders. It further provides achromatic variable retardance smectic liquid crystal retarders. The compound retarder of this invention comprises a central liquid crystal retarder unit and two external passive retarders positioned in series with and on either side of the liquid crystal retarder unit. The liquid crystal retarder unit comprises either (1) a rotatable smectic liquid crystal half-wave retarder or (2) first and second liquid crystal variable retarders having retardance switchable between zero and half-wave. The external passive retarders are equal in retardance and orientation to each other. Design equations determine the retardance of the external elements and their orientation relative to the central retarder to obtain a particular achromatic retardance for the compound structure.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.08/419,593, filed Apr. 7, 1995, now U.S. Pat. No. 5,658,490 incorporatedby reference in its entirety herein.

FIELD OF THE INVENTION

The present invention relates to compound retarders comprising liquidcrystal active retarders acting in combination with passive retarders tobehave as a single achromatic retarder.

BACKGROUND OF THE INVENTION

Liquid crystal retarders are increasingly utilized within opticaldevices such as tunable filters, amplitude modulators and lightshutters. Planar aligned smectic liquid crystal devices function asrotative waveplates wherein application of an electric field rotates theorientation of the optic axis but does not vary the birefringence. Incontrast, homeotropically aligned smectic liquid crystals, homogeneousaligned nematic devices, and nematic π-cells function as variableretarders, wherein application of an electric field varies thebirefringence. Chromaticity is a property of birefringent elements,passive and liquid crystal. There are two main components tochromaticity: (1) dispersion, which is the change in the birefringence(Δn) with wavelength λ; and (2) the explicit dependence of retardance on1/λ due to the wavelength dependent optical pathlength. Both componentscontribute to increased birefringence with decreased wavelength. Abirefringent material having a particular retardance at a designwavelength has higher retardance at shorter wavelengths and lowerretardance at longer wavelengths. Chromaticity places limitations on thespectral operating range of birefringent optical devices.

Chromaticity compensation for passive retarders was addressed by S.Pancharatnam, Proc. Indian Acad. Sci. A41, 137 [1955], and by A. M.Title, Appl. Opt. 14, 229 [1975], both of which are herein incorporatedby reference in their entirety. The wavelength dependence of passivebirefringent materials can be reduced by replacing single retarders withcompound retarders. The principle behind an achromatic compound retarderis that a stack of waveplates with proper retardance and relativeorientation can be selected to produce a structure which behaves as apure retarder with wavelength insensitive retardance. Pancharatnamshowed, using the Poincare sphere and spherical trigonometry, that sucha device can be implemented using a minimum of three films of identicalretarder material. A Jones calculus analysis by Title (supra) verifiedthe conditions imposed on the structure in order to achieve this result:(1) the requirement that the composite structure behave as a pureretarder (no rotation) forces the input and output retarders to beoriented parallel and to have equal retardance; and (2) first-orderstability of the compound retarder optic axis and retardance withrespect to wavelength requires that the central retarder be a half-waveplate. These conditions yield design equations that determine theretardance of the external elements and their orientation relative tothe central retarder for a particular achromatic retardance. Becausethese design equations specify a unique orientation of the centralretarder and a unique retardance for the external retarders, they havenever been applied to active liquid crystal devices and the problem ofactive retarder chromaticity remains.

For the specific example of an achromatic half-wave retarder, the designequations dictate that the external retarders are also half-wave platesand that the orientation of the external retarders relative to thecentral retarder is π/3. By mechanically rotating the entire structure,wavelength insensitive polarization modulation is feasible. Furthermore,Title showed that the compound half-wave retarder can be halved, and onesection mechanically rotated with respect to the other half to achieveachromatic variable retardance. Electromechanical rotation of suchcompound half-wave retarders has been used extensively to tunepolarization interference filters for astronomical imagingspectrometers.

The primary application of ferroelectric liquid crystals (FLCs) has beenshutters and arrays of shutters. In the current art, on- and off-statesof an FLC shutter (FIG. 1) are generated by reorienting the optic axisof FLC retarder 10 between π/4 and 0 with respect to bounding crossed orparallel polarizers 20 and 22. In the off-state, x-polarized light isnot rotated by the liquid crystal cell and is blocked by the exitpolarizer. In the on-state the polarization is rotated 90° and istherefore transmitted by the exit polarizer.

For maximum intensity modulation, the cell gap is selected to yield ahalf-wave retardance at the appropriate design wavelength. The on-statetransmission of x-polarized light is theoretically unity at the designwavelength, neglecting absorption, reflection and scattering losses. Atother wavelengths the transmission decreases. The ideal transmissionfunction for an FLC shutter as in FIG. 1 is given by ##EQU1## where δ isthe deviation from half-wave retardance with wavelength. This expressionindicates a second-order dependence of transmission loss on δ. Theoff-state transmission is in principle zero, but in practice it istypically limited to less than 1000:1 due to depolarization by defects,the existence of multiple domains having different alignments, andfluctuations in the tilt-angle with temperature.

High transmission through FLC shutters over broad wavelength bands isfeasible for devices of zero-order retardance, but it is ultimatelylimited by the inverse-wavelength dependence of retardation and therather large birefringence dispersion of liquid crystal materials. Forinstance, a visible FLC shutter device that equalizes on-state loss at400 nm and 700 nm requires a half-wave retarder centered at 480 nm. Azero-order FLC device with this retardance, using typical FLCbirefringence data, has a thickness of roughly 1.3 microns. Thetransmission loss at the extreme wavelengths, due to the departure fromhalf-wave retardance, is approximately 40%. This significantly limitsthe brightness of FLC displays and the operating band of FLC shuttersand light modulators. In systems incorporating multiple FLC devices,such as tunable optical filters or field-sequential display colorshutters, this source of light loss can have a devastating impact onoverall throughput and spectral purity.

SUMMARY OF THE INVENTION

This invention provides achromatic liquid crystal compound retarders,achromatic polarization switches, and achromatic shutters using theliquid crystal compound retarders. It further provides achromaticvariable retarders utilizing smectic liquid crystals. An achromaticshutter according to this invention is demonstrated which providesexcellent on-state transmission over the entire visible, ≧94% from 400nm to 700 nm after normalization for polarizer loss, and high contrast,1000:1 from 450 nm to 650 nm.

The smectic liquid crystal compound retarder of this invention comprisesa central rotatable smectic liquid crystal half-wave retarder and twoexternal passive retarders positioned in series with and on either sideof the liquid crystal retarder. The external retarders are equal inretardance and oriented parallel to each other. Design equationsdetermine the retardance of the external elements and their orientationrelative to the central retarder to obtain a particular retardance forthe compound structure. A reflection-mode compound achromatic retarderis constructed with a smectic liquid crystal quarter-wave retarderpositioned between a single passive retarder and a reflector.

In the compound retarders of this invention there is, in general, anorientation of the central liquid crystal retarder for which thestructure has maximum achromaticity in both orientation and retardance.Application of an electric field to the smectic liquid crystal cellrotates the optic axis between two or more orientations, one of whichprovides maximum achromaticity. Important aspects of this invention arethe discoveries that (1) the composite retardance at the designwavelength does not change with rotation of the central liquid crystalretarder and (2) there are orientations of the central liquid crystalretarder for which the optic axis of the compound retarder is stableeven though the composite retardance is not achromatic.

These properties are utilized in the achromatic polarization switch ofthis invention, comprising a linear polarizer and the compoundachromatic retarder, and in the achromatic shutter of this invention,comprising the compound achromatic retarder positioned between a pair ofpolarizers. In one switching state (the "on-state") the compoundretarder is achromatic and in a second state (the "off-state") thecompound retarder is oriented parallel to one polarizer and the lighttherefore does not "see" this retarder. In the off-state fixedretardance with wavelength is therefore not necessary. Providingachromatic orientation of the compound retarder in the off-state yieldshigh contrast shutters. Reflection-mode shutters are further provided inthis invention.

In alternative embodiments of the liquid crystal compound retarder, therotatable smectic liquid crystal half-wave retarder is replaced by firstand second liquid crystal variable birefringence retarders. The firstand second variable birefringence retarders have first and second fixedoptic axis orientations, respectively, and retardances which can beswitched between zero and half-wave. In operation, when one retarder isswitched to zero retardance, the other is switched to half-wave, andvice-versa, so that the composite retardance of the pair is a half-waveretardance with orientation switchable between the first and secondoptic axis orientations.

The achromatic variable retardance smectic liquid crystal compoundretarder of this invention comprises an active section rotatable withrespect to a passive section. The active section comprises two liquidcrystal retarders: a half-wave plate and a quarter-wave plate orientedat angles α₂ and α₂ +π/3, respectively, where the angle α₂ iselectronically switchable. The passive section comprises two retarders:a quarter-wave plate and a half-wave plate oriented at angles α₁ and α₁+π/3, respectively, where the angle α₁ is fixed. The quarter-wave platesare positioned between the half-wave plates. The composite retardance ofthe compound structure is 2(π/2-α₂ +α₁). To vary the retardance, theliquid crystal retarders in the active section are both rotated.

The planar aligned smectic liquid crystal cells of this invention havecontinuously or discretely electronically rotatable optic axes. Thesmectic liquid crystal cells can utilize SmC* and SmA* liquid crystals,as well as distorted helix ferroelectric (DHF), antiferroelectric, andachiral ferroelectric liquid crystals. The variable birefringence liquidcrystal cells of this invention can include homogeneously alignednematic liquid crystals, π-cells, and homeotropically aligned smecticliquid crystal cells.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a light shutter comprising a ferroelectric liquid crystalbetween crossed polarizers.

FIG. 2, comprising FIGS. 2a-2b, is an achromatic active compoundretarder comprising (a) a rotatable smectic liquid crystal half-waveplate and two passive retarders or (b) two liquid crystal variableretarders and two passive retarders.

FIG. 3 is an achromatic active compound retarder in reflection mode,comprising a rotatable smectic liquid crystal quarter-wave plate, apassive retarder, and a reflector.

FIG. 4 is an achromatic shutter utilizing an achromatic compoundretarder between crossed polarizers.

FIG. 5, comprising FIGS. 5a-5d, is the calculated on- and off-statetransmission spectra of crossed polarizer shutters having (a) anachromatic compound retarder and (b) a single retarder, and of parallelretarder shutters having (c) an achromatic compound retarder and (d) asingle retarder.

FIG. 6 is the measured on-state transmission spectra of (a) acompound-retarder achromatic shutter and (b) a single-retarder shutter.

FIG. 7 is the measured off-state transmission spectrum of acompound-retarder achromatic shutter.

FIG. 8 is the calculated on-state transmission of (a) acompound-retarder achromatic shutter and (b) a single-retarder shutteras a function of the deviation from half-wave retardance, δ.

FIG. 9 is the calculated off-state transmission of a compound-retarderachromatic shutter as a function of δ.

FIG. 10 is the calculated contrast ratio of a compound-retarderachromatic shutter as a function of δ.

FIG. 11, comprising FIGS. 11a-11b, is the calculated on- and off-statetransmission spectra of an achromatic shutter utilizing a compoundquarter-wave retarder.

FIG. 12, comprising FIGS. 12a-12b, shows multiple-pixel reflection-modeachromatic shutters having (a) parallel polarizers and (b) crossedpolarizers.

FIG. 13 is multiple-pixel transmission-mode achromatic shutter.

FIG. 14 is a compound achromatic variable retarder comprising a pair ofliquid crystal retarders and a pair of passive retarders.

DETAILED DESCRIPTION OF THE INVENTION

The elements in the devices of this invention are optically coupled inseries. The orientation of a polarizer refers to the orientation of thetransmitting axis, and the orientation of a birefringent element refersto the orientation of the principal optic axis of that element.Orientations are herein defined with respect to an arbitrary axis in aplane perpendicular to the light propagation axis. In the illustrationsof birefringent elements, the orientation is shown by arrow-headed linesand the retardance is labeled on the side of the element. When theretardance is switchable between two values, the values are both labeledon the side and are separated by a comma. The retardance refers to theretardance at a design wavelength. Note that a π retardance is equal toa half-wave (λ/2) retardance.

The term fixed retarder refers to a birefringent element wherein theorientation and retardance are not electronically modulated. Rotatableliquid crystal retarders of this invention have electronically rotatableorientation and fixed retardance at the design wavelength. Liquidcrystal variable retarders or, equivalently, liquid crystal variablebirefringence retarders have electronically variable retardance(birefringence) and fixed orientation. The term compound retarder isused for a group of two or more retarders which function as a singleretarder. The composite retardance of a compound retarder ischaracterized by an orientation and a retardance.

The terms design wavelength and design frequency (υ₀) refer to thewavelength and frequency at which the individual retarders within thecompound retarder provide the specified retardance. The term achromaticretarder refers to a retarder with minimal first-order dependence ofboth the retardance and the orientation on the deviation of the incidentlight from the design frequency (Δυ/υ₀). The term achromatic orientationrefers to an orientation of the optic axis with minimal first-orderdependence on the deviation of the incident light from the designfrequency.

A first embodiment of the liquid crystal achromatic compound retarder ofthis invention (FIG. 2a) comprises planar-aligned smectic liquid crystalretarder 30 having an orientation which is electronically rotatablebetween angles α₂ and α₂ '. These orientations are herein termed theon-state and the off-state, respectively. Retarder 30 provides ahalf-wave retardance (Γ₂ ⁰ =π) at the design wavelength. Passive outerretarders 40 and 42, with orientation α₁ and retardance Γ₁ ⁰ at thedesign wavelength, are positioned on either side of central retarder 30.In an alternative embodiment, the outside retarders are crossed insteadof parallel. In this application the design equations are derived forthe case of parallel retarders. Analogous equations can be derived forcrossed retarders.

In this embodiment the liquid crystal is an FLC, but it can be anymaterial with an electronically rotatable optic axis, including planaraligned SmC* and SmA* liquid crystals, as well as distorted helixferroelectric (DHF), antiferroelectric, and achiral ferroelectric liquidcrystals. The retarder switches between at least two orientations, α₂and α₂ '. It can, depending on the liquid crystal employed and theelectric field applied, rotate continuously between a range oforientations including α₂ and α₂ ', switch between bistable states α₂and α₂ ', or be switched between two or more discreet but notnecessarily stable orientations.

In a second embodiment of the achromatic retarder (FIG. 2b), rotatableretarder 30 is replaced by variable retarders 31 and 33 having fixedorientations of α₂ and α₂ ', respectively. The retardance of 31 and 33can be switched between zero and half-wave. The retardances aresynchronously switched, which as used herein means that when one haszero retardance the other has half-wave retardance and vice-versa. Thusthe composite retardance of 31 and 33 is always a half-wave and thecomposite orientation is switchable between α₂ and α₂ '.

Liquid crystal variable retarders 31 and 33 can include, but are notlimited to, homogeneously aligned nematic cells, nematic π-cells, andhomeotropically aligned smectic liquid crystal retarders. As is known inthe art, homogeneously aligned nematic cells and nematic π-cells aresometimes incapable of being electrically driven to zero retardance. Inthis case, the liquid crystal cell can be combined ("shimmed") with apassive retarder to compensate for the residual retardance. The passiveretarder is oriented orthogonal to the liquid crystal retarder if thebirefringence has the same sign and parallel if the birefringence hasopposite sign. In the present invention, variable retarders 31 and 33optionally include passive retarders to compensate for non-zero residualretardance.

This invention is described herein with the rotatable retarder (FIG. 2a)as the representative species of FIGS. 2a-b. It is to be understood thatin all embodiments of the present invention, a liquid crystal rotatableretarder can, in the manner of FIG. 2b, be replaced by a pair of liquidcrystal variable retarders. The species of FIG. 2a is preferred forseveral reasons. The construction is simpler because it uses a singleliquid crystal cell instead of two active cells. In addition, theswitching speed of smectic liquid crystals is orders of magnitude fasterthan nematics. Finally, the field of view is greater.

The passive outer retarders can be any birefringent material. Suitablematerials include crystalline materials such as mica or quartz,stretched polymeric films such as mylar or polycarbonates, and polymerliquid crystal films. In a preferred embodiment, the dispersion of thepassive retarders is approximately matched to the liquid crystaldispersion. Mylar, for example, has a similar dispersion to some FLCs.

The compound retarder of this invention is designed to be achromatic inthe on-state when the central retarder is oriented at α₂. Forachromaticity of the orientation and retardance, one solution for therelative orientations of the retarders is:

    cos 2Δ=-π/2Γ.sub.1.sup.0                    (2)

where Δ=α₂ -α₁. In addition there are isolated orientations for specificdesign frequencies that also yield achromatic orientation andretardance. The retardance, Γ, of the compound retarder is obtained from##EQU2## The orientation, Ω+α₁, of the compound retarder is obtainedfrom ##EQU3## where Ω is the orientation of the compound retarder withrespect to the orientation of the outside passive retarders.

Based on the above design equations, the retardance of the passiveretarders and the relative orientations of the retarders can be chosento provide the desired retardance of the compound retarder and to ensureachromaticity. For example, for an achromatic compound half-waveretarder (Γ=π), Eq. 3 provides the solution Γ₁ ⁰ =π, and Eq. 2 providesthe relative orientation of the retarders as Δ=60°. Eq. 4 gives therelative orientation of the compound retarder as Ω=30°. Therefore, toobtain an orientation of Ω=α₁ =45° for the compound half-wave retarder,the passive retarders are oriented at α₁ =15°. Since Δ=60°, theorientation of the central retarder must then be α₂ =75°. Similarly, foran achromatic compound quarter-wave retarder (Γ=π/2), the equationsyield Γ₁ ⁰ =115°, Δ=71°, and Ω=31°. Thus, for an orientation of Ω+α₁=45°, the passive retarders are oriented at α₁ =14° and the centralretarder is at α₂ =85°.

In the achromatic compound retarder of this invention, the liquidcrystal central retarder has an optic axis rotatable between α₂ and α₂'. When the liquid crystal retarder is at α₂ ', the orientation relativeto the outer retarders is Δ'=α₂ '-α₁ and the orientation of the compoundretarder relative to the outer retarders is Ω'. Since Eq. 2 gives aunique solution for the absolute value of Δ, at which the compoundretarder is achromatic, it teaches against changing the orientation ofthe central retarder with respect to the outer retarders. An aspect ofthe present invention is the discovery that (1) at orientations α₂ ' ofthe central retarder which do not satisfy Eq. 2, the compositeretardance Γ is nevertheless unchanged at the design wavelength and (2)there are orientations α₂ ' of the central retarder for which, eventhough the composite retarder is not achromatic, the optic axis isstable with respect to wavelength. A further aspect of this invention isthe realization that in many devices the composite retardance does notaffect device output in certain switching states and therefore it neednot be achromatic in those states. In particular, when the compoundretarder is oriented parallel to a polarizer, the polarized light is notmodulated by the retarder and hence any chromaticity of the retardanceis unimportant. Only stability of the optic axis is required so that theorientation remains parallel to the polarizer throughout the operatingwavelength range. These properties lead to numerous useful devicesutilizing the compound retarder with a rotatable central retarder.

In a preferred embodiment of the retarder, the orientation is achromaticwhen the liquid crystal retarder is oriented at α₂ '. The first orderterm of the frequency dependence of the orientation of the retardationaxis is ##EQU4## where ε is the relative frequency difference Δυ/υ₀.Note that in the on-state, wherein Eq. 2 is satisfied, Eq. 5 gives∂Ω/∂ε=0. This confirms that the on-state orientation is achromatic. Foroff-state orientations, α₂ ', Eq. 5 can be used to determine themagnitude of ∂Ω'/∂ε. For the special case of an achromatic half-waveretarder, Γ₁ ⁰ =π, and sin Γ₁ ⁰ =0, so ∂Ω/∂ε=0 for all values of α₂ ',i.e. the orientation is achromatic at all orientations.

Because of the symmetry of the achromatic retarder, it can beimplemented in reflection-mode, as illustrated in FIG. 3. Thereflection-mode embodiment of the retarder of FIG. 2a utilizes a singlepassive retarder 40, with retardance Γ₁ ⁰ and orientation α₁, liquidcrystal quarter-wave retarder 32, with orientation switchable between α₂and α₂ ', and reflector 50. Because the reflector creates a second passthrough the liquid crystal quarter-wave retarder, the net retardance ofthe liquid crystal cell is a half wave. A forward and return passthrough the reflection-mode device is equivalent to a single passthrough the compound retarder of FIG. 2a. The reflection-mode embodimentof the retarder of FIG. 2b uses a pair of variable retarders switchablebetween zero and quarter-wave retardance in lieu of rotatablequarter-wave retarder 32 in FIG. 3. The reflector in the embodimentshown in FIG. 3 has R=1 but it can also have R<1. The reflector cantransmit an optical signal for addressing the liquid crystal retarder.

This invention further includes devices employing the achromaticcompound retarder described above. The polarization switch of thisinvention comprises a linear polarizer in combination with theachromatic compound retarder. The polarizer can be neutral withwavelength or can be a pleochroic polarizer. Light is linearly polarizedby the polarizer and the polarization is modulated by the compoundretarder. For the case of a half-wave retarder, the polarization remainslinear and the orientation is rotated. Other retarders produceelliptically polarized light. The polarization switch functions as apolarization receiver when light is incident on the retarder rather thanthe polarizer. In the preferred embodiment, the compound retarder isachromatic in the on-state (α₂) and is oriented parallel to thepolarizer in the off-state (α₂ '). With this preferred off-stateorientation achromaticity in the composite retardance is not neededbecause, with the orientation parallel to the polarizer, the polarizedlight does not "see" the compound retarder and is not modulated by it.In a more preferred embodiment, the orientation of the compound retarderis stable in the off-state, i.e., ∂Ω'/∂ε is small. In the most preferredembodiment the orientation is achromatic, i.e., ∂Ω'/∂ε is zero.

A particularly useful embodiment of the polarization switch isillustrated in FIG. 4. The polarization switch 110 comprises polarizer20, outer retarders 40 and 42, and liquid crystal retarder 30. Passiveretarders 40 and 42 are half-wave retarders (Γ₁ =π) oriented at α₁=π/12. Liquid crystal half-wave plate 30 is switchable between on- andoff-state orientations of α₂ =5π/12 and α₂ '=8π/12, respectively. Thisgives a compound retardance Γ=λ/2 and orientations Ω+α₁ =π/4 and Ω'+α₁=0. In the off-state light remains polarized along the x-axis and in theon-state it is oriented parallel to the y-axis. Because the compoundhalf-wave retarder has an achromatic orientation for all values of α₂ ',it can be used to achromatically rotate the polarization between theinput polarization and any other linear polarization.

The polarization switch can be used in combination with any polarizationsensitive element. In combination with an exit polarizer it forms anachromatic shutter. The achromatic shutter of FIG. 4 employs polarizers20 and 22. In this embodiment they are crossed but they canalternatively be parallel. This shutter is analogous to the shutter ofFIG. 1: the compound retarder has a half-wave retardance, and on- andoff-state composite retarder orientations of π/4 and 0, respectively.Like the shutter of FIG. 1, the shutter of FIG. 4 requires only oneactive retarder. The advantage is that the shutter of this invention isachromatic.

A mathematical analysis of the compound half-wave retarder and theshutter demonstrates the wavelength stability of the devices of thisinvention. The Jones matrix for the compound half-wave retarder is theproduct of the matrices representing the three linear retarders. TheJones matrix that propagates the complex cartesian field amplitude isgiven by chain multiplying the matrices representing the individuallinear retarders. For the on- and off-states these are given,respectively, by the equations

    W.sub.c (π/4)=W(π+δ,π/12)W(π+δ,5π/12)W(π+δ,.pi./12)                                                      (6)

and

    W.sub.c (0)=W(π+δ,π/12)W(π+δ,2π/3)W(π+δ,π/12)(7)

where the general matrix for a linear retarder with retardation Γ andorientation α is given by ##EQU5## and the absolute phase of eachretarder is omitted. For the present analysis, each retarder is assumedidentical in material and retardance, with half-wave retardation at aspecific design wavelength. This wavelength is preferably selected toprovide optimum peak transmission and contrast over the desiredoperating wavelength band. The retardance is represented here by theequation Γ=(π+δ), where δ is the wavelength dependent departure from thehalf-wave retardance. For the present work, the dispersion is modeledusing a simple equation for birefringence dispersion that is suitablefor both FLC and the polymer retarders used (Wu, S. T., Phys. Rev.(1986) A33:1270). Using a fit to experimental FLC and polymerspectrometer data, a resonance wavelength was selected that suitablymodels the dispersion of each material.

Substituting the three matrices into Eqs. 6 and 7 produces on- andoff-state matrices that can be written in the general form ##EQU6##where |t_(ij) | denotes the magnitude and θ the phase of the complext_(ij) matrix components of the compound structure. The specificelements for the (achromatic) on-state are given by ##EQU7## Thecomponents for the off-state are given by ##EQU8##

In the shutter device the compound retarder is placed between crossedpolarizers. The Jones vector for the transmitted field amplitude isgiven by the matrix equation

    E(λ)=P.sub.y W.sub.c P.sub.x E.sub.o (λ).    (16)

The polarizers are taken to be ideal ##EQU9## and the input fieldspectral density, E_(o) (λ) is taken to be x polarized, with unityamplitude. Under these conditions, the Jones vector for the transmittedfield is the off-diagonal component of W_(c). The y component of theoutput Jones vector gives the field transmittance of the structure.

Since the components of W_(c) are given above in terms of theirmagnitudes, the intensity transmission of the on- and off-states of thecompound retarder are given by simply squaring the off-diagonal terms ofEqs. 11 and 14, or T=|t₁₂ |². This gives the two intensity transmissionfunctions of the shutter ##EQU10##

The above outputs illustrate the desirable result that the second orderdependence of transmitted intensity on δ vanishes. The loss intransmission in the on-state and the leakage in the off-state have atmost a fourth-order dependence on δ.

Like a simple FLC shutter, the mechanism for modulating polarizationwith the smectic liquid crystal compound retarder is by rotating theorientation of the compound retarder rather than by varying thebirefringence. This can clearly be seen by considering wavelength bandssufficiently narrow that the second (and higher) order terms of theJones matrices in δ can be neglected. In this instance the matricesrepresenting on- and off-states reduce respectively to ##EQU11##

The on-state matrix reduces, to this degree of approximation, to anideal achromatic half-wave retarder oriented at π/4, while the off-statematrix reduces to an ideal linear retarder oriented at 0, withretardation 2θ. Since only an off-diagonal component is utilized in ashutter implementation, the output is ideal to this degree ofapproximation.

The elimination of the second order term is achieved using a 3-elementstructure that achieves ideal half-wave retardation at two wavelengths,rather than a single wavelength for the simple FLC shutter. Thisbehavior can be seen by slightly varying the relative orientation of thecentral and exterior retarders in the on-state. The two idealtransmission states, as well as the two null states, can be furtherseparated in this way, increasing the operating band but producing amore pronounced dip (leakage) between maxima (nulls).

Based on the above equations, comparisons can be drawn between thecompound retarder shutter and the conventional FLC shutter. A 10% lossin transmission for a conventional shutter occurs for a retardationdeviation of δ=37°, while the same loss for the achromatic shutteroccurs for δ=72°.This is very nearly a factor of two increase in δ.Using a computer model for the structures, the transmission spectrum(FIG. 5a) for an achromatic shutter optimized for visible operation(400-700 nm) has a 90% transmission bandwidth of 335 nm (409-744 nm),while the spectrum (FIG. 5b) for a conventional shutter with a designwavelength of 480 nm has a 90% bandwidth of 122 nm (433-555). The resultis a factor of 3.75 increase in bandwidth. Calculated spectra forparallel polarizer shutters with a compound retarder (FIG. 5c) and asingle retarder (FIG. 5d) show the tremendous improvement in theoff-state provided by the achromatic retarder of this invention.

The increase in operating bandwidth is accompanied by a theoretical lossin contrast ratio. The first order stability requirement of the opticaxis allows off-state leakage due to the presence of higher order terms.In practice, little if any actual sacrifice is observed whenincorporating the compound retarder. An FLC optimized for visibleoperation (half-wave at 480 nm) gives a maximum departure in retardanceof δ=75°. Using this value, and assuming that the external retardershave dispersion identical to FLC, a worst-case contrast ratio of 667:1is found for operation in the 400-700 nm band. For most of this band,theory predicts contrast far in excess of 1000:1.

The conventional and the achromatic shutters were experimentallydemonstrated to verify the performance predicted by computer modeling.The FLC device was fabricated using ZLI-3654 material from E-Merck. TheITO coated substrates were spin coated with nylon 6/6 and were rubbedunidirectionally after annealing. Spacers with a diameter of 1.5 micronswere dispersed uniformly over the surface of one substrate and UV cureadhesive was deposited on the inner surface of the other substrate. Thesubstrates were gapped by applying a uniform pressure with a vacuum bagand subsequently UV cured. The FLC material was filled under capillaryaction in the isotropic phase and slowly cooled into the C* phase. Aftercooling, the leads were attached to the ITO and the device wasedge-sealed. The FLC cell had a half-wave retardance at 520 nm.

A conventional shutter as in FIG. 1 was formed by placing the FLC cellwith the optic axis oriented at 45° between parallel polarizers.Polaroid HN22 polarizers were used due to their high contrast throughoutthe visible. The structure was probed by illuminating with a 400 W Xenonarc lamp, and the transmitted light was analyzed using a SPEX 0.5 mgrating spectrometer system. The on-state transmission is shown in FIG.6b.

The achromatic shutter was subsequently assembled using the same FLCdevice positioned between two Nitto NRF polycarbonate retarders havinghalf-wave retardance of 520 nm. Since the FLC device is not dispersionmatched to the polymer film, a loss in contrast ratio is anticipated forthe compound retarder due to increased off-state leakage. Thepolycarbonate films were oriented at 15° with respect to the inputpolarizer, which was crossed with the exit polarizer. The FLC wasswitched between orientations of 5π/12 and 8π/12. The on-state (FIG. 6a)and off-state (FIG. 7) spectra were measured. Both of these spectra wereappropriately normalized to remove leakage due to non-ideal polarizers,depolarization by retarders, and the polarization dependence of the lampspectrum.

The measured transmission spectra indicate excellent agreement with themodel results. FIG. 6 is a striking demonstration of the increasedtransmission over the visible spectrum provided by the achromaticshutter of this invention.

The model was further used to calculate the on-state transmission of acompound-retarder achromatic shutter (Eq. 19) and a single retardershutter (Eq. 1) as a function of δ, the deviation from half-waveretardance. The calculated transmission spectra are shown is FIG. 8.FIG. 9 is the calculated off-state transmission of a compound-retardershutter as a function of δ, and FIG. 10 is the calculated contrastratio.

Using the achromatic shutter at slightly longer center wavelengths,where FLC dispersion is greatly reduced, enormous operating bands arefeasible. For instance, the calculated 95% transmission bandwidth of ashutter centered at 600 nm is approximately 400 nm (480 nm-880 nm),while that for a simple FLC shutter is only 150 nm (540 nm-690 nm).

Achromatic polarization switches and shutters of this invention can alsoutilize compound retarders with composite retardances other thanhalf-wave. For example, a polarization switch can be fabricated using alinear polarizer and a compound quarter-wave retarder. In oneembodiment, the orientation of the compound retarder switches betweenπ/4 and 0 with respect to the input polarizer, i.e. Ω+α₁ =45° and Ω'+α₁=0°. To achieve this, Eqs. 2-4 give Γ₁ ⁰ =115°, Δ=71°, α₁ =14° and α₂=85° in the on-state, and in the off-state Δ'=96°, and α₂ '=111°. In theon-state the compound quarter-wave retarder switches the linear light tocircularly polarized light and in the off-state the linear polarizationis preserved. Addition of a second polarizer perpendicular to the firstmakes a shutter which switches between 50% transmission in the on-stateand zero transmission in the off-state. The transmission spectra (FIGS.11a-b) were calculated assuming no dispersion. Note that the off-statetransmission spectrum is shown on a logarithmic scale in FIG. 11b.

The achromatic compound retarder, polarization switch and shutter ofthis invention have been illustrated with FLCs having two optic axisorientations. They can alternatively utilize more than two optic axisorientations and can have a continuously tunable optic axis.

The achromatic shutter of this invention can be utilized in applicationssuch as CCD cameras, eye protection systems, glasses in virtual realitysystems, three-color shutters in field-sequential display, beamsteerers,diffractive optics and for increasing the brightness of LC flat-paneldisplays.

For many display applications the achromatic shutter can be used in amultiple-pixel array, as shown in FIGS. 12 and 13. In these drawingsoptical elements are shown in cross section and are represented byrectangular boxes. The retardance of birefringent elements is listed inthe top of the box and the orientation is in the bottom. When elementscan rotate between two or more orientations, both orientations arelisted in the box and are separated by a comma.

Two reflection-mode embodiments are shown in FIG. 12. FLC retarder 32has a quarter-wave retardance at the design wavelength and the opticaxis is rotatable between 5π/12 and 8π/12. The FLC cell is formed withsubstrates 90 and 92. Voltages are applied to the FLC using transparentelectrode 95 and pixellated mirror electrodes 52. Each pixel can beseparately addressed to provide the desired display pattern. Thecompound retarder is formed by the FLC in combination with passivehalf-wave retarder 40, oriented at π/12.

In FIG. 12a the shutter array uses linear polarizer 20 oriented at 0.Since in reflection-mode polarizer 20 is both the input and outputpolarizer, this is a parallel polarizer embodiment. The array isilluminated by ambient light 100 and the viewer is represented by aneye. In FIG. 12b the array uses polarizing beam splitter 25 to create acrossed polarizer embodiment. White light 101 illuminates the array andmodulated gray light is output to the viewer.

A transmission-mode array is illustrated in FIG. 13. In this embodimentthe FLC has a half-wave retardance. Voltages are applied usingtransparent electrode 95 and pixellated transparent electrode 96. Thecompound retarder is formed by the FLC retarder in combination withouter retarders 40 and 42. The shutter is formed by polarizers 20 and 22which, in this embodiment, are crossed. The array is illuminated bybacklight assembly 103, which can be collimated by lens 104. The displayis viewed in transmission.

The achromatic compound retarder of this invention has been demonstratedwithin an achromatic shutter. In addition it can be used in many otheroptical devices known in the art. In particular, it is suited to devicesin which the retarder need be achromatic in only one orientation andwherein slight achromaticity in other orientations can be tolerated.Specific examples include polarization interference filters and dye-typecolor polarizing filters.

Numerous previous devices by the inventors can be improved by using theachromatic retarder of this invention. In the polarization interferencefilters of U.S. Pat. Nos. 5,132,826, 5,243,455 and 5,231,521, all ofwhich are herein incorporated by reference in their entirety, a smecticliquid crystal rotatable retarder and a passive birefringent element arepositioned between a pair of polarizers. In a preferred embodiment thebirefringent element is oriented at π/4 with respect to a polarizer. Inthe split-element polarization interference filters of U.S. patentapplication 08/275,006, filed Jul. 12, 1994, which is hereinincorporated by reference in its entirety, a center retarder unit and apair of split-element retarder units are positioned between a pair ofpolarizers. The retarder units can include a rotatable liquid crystalretarder. The individual liquid crystal rotatable retarders of theabove-mentioned polarization interference filters can be replaced withthe compound achromatic retarders of the present invention.

The liquid crystal handedness switch and color filters described in U.S.patent application 08/131,725, filed Oct. 5, 1993, which is hereinincorporated by reference in its entirety, can also be improved by usingthe achromatic retarders of the present invention. The circularpolarization handedness switch and the linear polarization switchcomprise a linear polarizer and a rotatable liquid crystal retarder. Thecolor filters use the polarization switch in combination with a colorpolarizer, such as a cholesteric circular polarizer or a pleochroiclinear polarizer. The simple liquid crystal rotatable retardersdescribed in the handedness switch invention can be replaced with thecompound achromatic retarders of the present invention.

The compound achromatic retarder can also be used to improve other colorfilters known in the art, for example as described in Handschy et al.,U.S. Pat. No. 5,347,378 which is herein incorporated by reference in itsentirety. These color filters comprise a linear polarizer and arotatable liquid crystal retarder. In some embodiments they furthercomprise pleochroic polarizers and in other embodiments they furthercomprise a second linear polarizer and a passive birefringent element.The simple liquid crystal rotatable retarder of the Handschy et al.invention can be replaced with the compound achromatic retarders of thepresent invention.

The color filters of this invention can be temporally multiplexed,wherein the output color is switched on a timescale which is rapidcompared to a slow response time detector, such as the human eye. Thecompound retarder of FIG. 2a employing the smectic liquid crystal cellis particularly suited to this application.

The criterion for replacing a single retarder with the achromaticcompound retarder of this invention is that the single retarder must berotatable between two or more orientations of the optic axis. Thecompound retarder is especially suited for use in devices wherein it ispositioned adjacent to a linear polarizer and wherein the orientation ofthe retarder is, in one of its switching states, parallel to the linearpolarizer. The achromaticity of the compound retarder is particularlyadvantageous in color filtering devices because it can increase thethroughput across the entire visible spectrum.

The compound retarder of this invention can also be used in opticaldevices to replace a pair of variable retarders wherein the first andsecond variable retarders have first and second fixed orientations andhave retardances switchable between first and second levels, and whereinthe retardances are synchronously switched between opposite levels. Inaddition, since the achromatic half-wave retarder can be used to rotatethe orientation of linearly polarized light, it can replace twistednematic cells in optical devices.

In addition to the compound achromatic retarder, this invention providesan achromatic variable retarder, illustrated in FIG. 14. An activesection comprises smectic liquid crystal half-wave retarder 60, orientedat α₂, and smectic liquid crystal quarter-wave retarder 65, oriented atα₂ +π/3. Angle α₂ of retarders 60 and 65 is electronically tuned,preferably synchronously. A passive section comprises passivequarter-wave retarder 75, oriented at α₁ +π/3, and passive half-waveretarder 70, oriented at α₁. Angle α₁ is fixed. The angle α₂ of theliquid crystal retarder orientation can be rotated discreetly orcontinuously to at least one other angle, α₂ '. The retardance of thecompound structure is 2(π/2-α₂ +α₁).

What is claimed is:
 1. An achromatic compound retarder, comprising:afirst passive retarder unit having a predetermined retardance at adesign wavelength and having a predetermined optic axis orientation; asecond passive retarder unit having the predetermined retardance at thedesign wavelength and having substantially the same predetermined opticaxis orientation as the first passive retarder unit; and a centralretarder unit positioned between the first and second passive retarderunits, the central retarder unit having a retardance of approximately πat the design wavelength and an optic axis orientation switchablebetween at least a first orientation state and a second orientationstate, wherein the compound retardance is substantially achromatic whenthe optic axis of the central retarder unit is in the first orientationstate.
 2. The achromatic compound retarder of claim 1, wherein the opticaxis orientation of the compound retarder is substantially achromaticwhen the optic axis of the central retarder unit is in the secondorientation state.
 3. The achromatic compound retarder of claim 1,wherein the central retarder unit comprises a planar-aligned retarderhaving an optic axis orientation which is electronically rotatablebetween at least the first orientation state and the second orientationstate.
 4. The achromatic compound retarder of claim 1, wherein thecentral retarder unit comprises a plurality of variable retarders havingfixed optic axis orientations, a first one of the variable retardershaving a first retardance at the first orientation state of the centralretarder unit, and a second one of the variable retarders having asecond retardance at the second orientation state of the centralretarder unit.
 5. The achromatic compound retarder of claim 4, whereinthe first retardance is approximately π and the second retardance isapproximately π.
 6. The achromatic compound retarder of claim 5, whereinat least one of the first and second ones of the variable retarders haveassociated passive retarders to compensate for non-zero residualretardance.
 7. The achromatic compound retarder of claim 1, wherein theoptic axis of the central retarder unit is adapted to rotatecontinuously between a range of orientations including the first andsecond orientations states.
 8. The achromatic compound retarder of claim1, wherein the optic axis of the central retarder is switchable betweenat least two discreet orientation states.
 9. The achromatic compoundretarder of claim 8, wherein the central retarder unit is bistable andthe at least two discreet orientation states are the first and secondorientation states.
 10. A polarization switch, comprising:the achromaticcompound retarder of claim 1; and a first linear polarizer opticallycoupled to the compound retarder.
 11. The polarization switch of claim10, wherein the second optic axis orientation state of the centralretarder unit is parallel to an orientation of the first linearpolarizer.
 12. An achromatic shutter, comprising:the polarization switchof claim 10, and a second linear polarizer optically coupled to thecompound retarder, the compound retarder being located optically betweenthe first and second linear polarizers.
 13. An achromatic compoundretarder, comprising:a passive retarder unit having a predeterminedretardance at a design wavelength and having a predetermined optic axisorientation; a reflector; and a central retarder unit positioned betweenthe passive retarder unit and the reflector, the central retarder unithaving a retardance of approximately π/2 at the design wavelength and anoptic axis orientation switchable between at least a first orientationstate and a second orientation state, wherein the compound retardance issubstantially achromatic when the optic axis of the central retarderunit is in the first orientation state.
 14. The achromatic compoundretarder of claim 13, wherein the optic axis orientation of the compoundretarder is substantially achromatic when the optic axis of the centralretarder unit is in the second orientation state.
 15. The achromaticcompound retarder of claim 13, wherein the central retarder unitcomprises a planar-aligned retarder having an optic axis orientationwhich is electronically rotatable between at least the first orientationstate and the second orientation state.
 16. The achromatic compoundretarder of claim 13, wherein the central retarder unit comprises aplurality of variable retarders having fixed optic axis orientations, afirst one of the variable retarders having a first retardance at thefirst orientation state of the central retarder unit, and a second oneof the variable retarders having a second retardance at the secondorientation state of the central retarder unit.
 17. The achromaticcompound retarder of claim 16, wherein the first retardance isapproximately π/2 and the second retardance is approximately π/2. 18.The achromatic compound retarder of claim 17, wherein at least one ofthe first and second ones of the variable retarders have associatedpassive retarders to compensate for non-zero residual retardance. 19.The achromatic compound retarder of claim 13, wherein the optic axis ofthe central retarder unit is adapted to rotate continuously between arange of orientations including the first and second orientationsstates.
 20. The achromatic compound retarder of claim 13, wherein theoptic axis of the central retarder is switchable between at least twodiscreet orientation states.
 21. The achromatic compound retarder ofclaim 20, wherein the central retarder unit is bistable and the at leasttwo discreet orientation states are the first and second orientationstates.
 22. A polarization switch, comprising:the achromatic compoundretarder of claim 16; and a linear polarizer optically coupled to thecompound retarder.
 23. The polarization switch of claim 22, wherein thesecond optic axis orientation state of the central retarder unit isparallel to an orientation of the polarizer.
 24. A method of impartingan achromatic retardance on a light beam, comprising:passing the lightbeam through a first passive retarder unit having a predeterminedretardance at a design wavelength and having a predetermined optic axisorientation; passing the light beam through a central retarder unit atleast once, the central retarder unit having an optic axis orientationswitchable between at least a first orientation state and a secondorientation state; and passing the light beam through one of the firstpassive retarder unit and a second passive retarder unit having thepredetermined retardance at the design wavelength and havingsubstantially the same predetermined optic axis orientation as the firstpassive retarder unit, wherein the retardance of the central retarderunit at the design wavelength is π divided by the number of passes thelight beam makes through the central retarder unit, and the retardanceimparted on the light beam is substantially achromatic when the centralretarder unit is in the first orientation state.
 25. The method of claim24, wherein the step of passing the light beam through a centralretarder at least once comprises the steps of:passing the light beamthrough the central retarder; and reflecting the light beam back throughthe central retarder.
 26. An achromatic compound retarder,comprising:means for passing a light beam through a first passiveretarder unit having a predetermined retardance at a design wavelengthand having a predetermined optic axis orientation; means for passing thelight beam through a central retarder unit at least once, the centralretarder unit having an optic axis orientation switchable between atleast a first orientation state and a second orientation state; andmeans for passing the light beam through one of the first passiveretarder unit and a second passive retarder unit having thepredetermined retardance at the design wavelength and havingsubstantially the same predetermined optic axis orientation as the firstpassive retarder unit, wherein the retardance of the central retarderunit at the design wavelength is π divided by the number of passes thelight beam makes through the central retarder unit, and the retardanceimparted on the light-beam is substantially achromatic when the centralretarder unit is in the first orientation state.